Discrete Ramanujan-Fourier Transform of Even Functions (mod $r$)
نویسنده
چکیده
An arithmetical function f is said to be even (mod r) if f (n) = f ((n, r)) for all n ∈ Z + , where (n, r) is the greatest common divisor of n and r. We adopt a linear algebraic approach to show that the Discrete Fourier Transform of an even function (mod r) can be written in terms of Ramanujan's sum and may thus be referred to as the Discrete Ramanujan-Fourier Transform.
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ورودعنوان ژورنال:
- CoRR
دوره abs/1210.0295 شماره
صفحات -
تاریخ انتشار 2012